Vol. 5, No.4, 2016 Hybrid Intelligent Approach for ...

Hybrid Intelligent Approach for Predicting ProductCompositions of a Distillation Column

Yousif Al-DunainawiElectronic and Computer Engineering Department

College of Engineering, Design and Physical Sciences Brunel University London

Uxbridge, London, UK

Maysam F. AbbodElectronic and Computer Engineering Department

College of Engineering, Design and Physical Sciences Brunel University London

Uxbridge, London, UK

Abstract—Compositions measurement is a vitally critical issuefor the modelling and control of distillation process. The productcompositions of distillation columns are traditionally measuredusing indirect techniques via inferring tray compositions from itstemperature or by using an online analyser. These techniqueswere reported as inefficient and relatively slow methods. Inthis paper, an alternative procedure is presented to predict thecompositions of a binary distillation column. Particle swarm opti-misation based artificial neural network PSO-ANN is trained bydifferent algorithms and tested by new unseen data to check thegenerality of the proposed method. Particle swarm optimisationis utilised, here, to choose the optimal topology of the network.The simulation results have indicated a reasonable accuracyof prediction with a minimal error between the predicted andsimulated data of the column.

Keywords—Hybrid Intelligence; Prediction; Distillation Col-umn; Neural network; Particle swarm optimisation

I. INTRODUCTION

Over the past few decades, great developments in onlineanalysis, monitoring and measurement of dynamic processeswere made in various applications [1]–[5]. This developmentis partially motivated by the desire to improve quality. Un-ambiguously, quality is a significant indication that has asubstantial impact on productivity and economy of manufac-ture, particularly in the field of mass production [2]. Directmeasurement of the product compositions of the distillationcolumn is a crucial issue. However, its disadvantages at streamprocess lie in difficulty, unreliability and high capital andoperational cost. These disadvantages will have an exponen-tially negative effect when more than one analysis are neededto obtain a clearer picture of the different streams involved.Consequently, indirect and inferential measurement techniquesare being used to design and run many distillation columns.These columns operate widely in chemical and petrochemicalplants as well as refineries to separate mixtures into theirindividual components.

Not only non-linearity and transit behaviour make distil-lation, as a process, complicated to control, but the productcompositions also cannot be promptly measured, nor reliable.The delay caused by the measurement and analysis of compo-sitions will negatively affect the effectiveness and robustnessof control [6]. An indirect method is proposed to monitor theproducts compositions of the column by using tray temperatureinside the column, albeit this feature is an unreliable indicator

of product compositions [7], [8]. Moreover, other consider-ations like consistent maintenance, regular calibrations, andhigh-cost equipment make composition analysers an ineffectivesolution for precise online measurements. Consequently, softsensing or inferential systems have been proposed recently aspractical options to replace hardware measurement systems [9].

Artificial neural networks (ANNs) is one of the mostattention-grabbing branches of artificial intelligence, whichhas grown rapidly in the recent years as an optimal solu-tion for the modelling, and prediction of dynamic systems.ANNs have shown outstanding performance to learn the input-output relationship of nonlinear and complex systems. Thisrelationship could be easily, quickly and efficiently found outvia reducing the error between the network output(s) andthe actual output(s). After the network is trained, the outputcan be predicted within few seconds. ANN-based modelsare still being applied successfully to overcome engineeringproblems in different fields such as adaptive control, patternrecognition, robotics, image processing, medical diagnostics,fault detection, process monitoring, renewable and sustainableenergy, laser applications and nonlinear system identification[10]–[17].

The most crucial task which faces the neural networkconstructer is the proper selection of the network topologyto solve a particular problem. The topology means, here, thenumber of nodes (neurones) and the number of layers in thehidden zone. Therefore, one of the most efficient methodsto determine the optimal network structure is evolutionaryalgorithm EA methods such as genetic algorithm GA [18] andpractical swarm optimisation PSO [19] and so on.

This paper proposed a PSO-based neural network as apredictor model for estimating the product compositions ofa binary distillation column.

II. DISTILLATION COLUMN MODELLING ANDDESCRIPTION

Distillation is, undoubtedly, one of the most importantprocesses in chemical and petrochemical plants. Distillationcolumns are used as separators of chemical compounds inpetroleum, natural gas, liquid and chemical industries [20].The major disadvantage of using those columns is that they areconsidered as an intensive energy process. A report from theUS Department of Energy has indicated that distillation is the

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largest consumer of energy in the chemical industry; typically,it accounts 40% of the energy consumed by petrochemicalplants. Despite its “thirst” for energy, distillation persists to bea widely utilised method for separations [21], [22].

Figure 1 is a schematic diagram of a binary distillationcolumn, in which a feed mixture is separated into a distil-late product (overhead) and a bottom product. Also, heat istransferred into the column via a reboiler (heat exchanger) tovaporise some of the liquid from the base of the column. Thevapour travels up through trays inside the column to reach thetop and, then, comes out to be liquefied in a condenser. Liquidfrom the condenser, at that point, drops into the reflux drum.Finally, the distillate is removed from this drum as a pureproduct. additionally, some liquid (reflux) is fed back near thetop of the column while the impure product is produced at thebottom outlet.

Fig. 1: Schematic diagram of a binary distillation column

The dynamic model can be simplified under the followingassumptions:

• No chemical reactions occur in all stages of thecolumn

• Constant pressure (open to atmosphere pressure)

• Binary mixture

• Constant relative volatility

• No vapour hold-up occurs

• Perfect mixing and equilibrium for vapour-liquid onall stages

While the operating conditions and technical aspects of thedistillation column are detailed in the appendix at the end ofthis paper.

Accordingly, the mathematical expression of the model canbe represented with the assumptions by the following equa-tions: On each tray (excluding reboiler, feed and condenserstages):

• On each tray (excluding reboiler, feed and condenserstages):

Midxit

= Li+1xi+1 + Vi−1yi−1 − Lixi − Viyi (1)

• Above the feed stage i = NF + 1:

Midxit

= Li+1xi+1+Vi−1yi−1−Lixi−Viyi+FV yF(2)

• Below the feed stage i = NF :

Midxit

= Li+1xi+1+Vi−1yi−1−Lixi−Viyi+FLXF

(3)

• In the reboiler and column base i = 1, xi = xB:

MBdxit

= Li+1xi+1 − Viyi +BxB (4)

• In the condenser, i = N + 1, xD = xN + 1:

MDdxit

= Vi−1yi−1 − LixD −DxD (5)

• Vapour-liquid equilibrium relationship for each tray[23]:

yi =αxi

1 + (α− 1)xi(6)

• The flow rate at constant molar flow:

Li = L, V i = V + FV (7)

sinceFL = qF × F (8)

Fv = F + FL (9)

• The flowrate of both condenser and reboiler as: Re-boiler:

B = L+ FL − V (10)

Condenser:D = V + FV − L (11)

• The feed compositions xF and yF are found from theflash equation as:

FzF = FL × xF − FV × yF (12)


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III. HYBRID MODEL DEVELOPMENT AND OPTIMISATION

Recently, hybridization or combination of different learningand adaptation techniques has been employed to a largenumber of new intelligent system designs. The main aim ofintegrating these techniques is to overcome individual limita-tions and to achieve synergetic effects [24].

Therefore, a PSO-based artificial neural network is pro-posed as an estimator tool of a binary distillation column.

A. Artificial Neural Networks

Artificial neural network (ANNs) is a complicated system,which is composed of numerous neural nets. These nets funda-mentally based on the principal understanding of the function,structure, and the mechanism of the brain of humankind [25].In the last two decades or so, ANNs have been applied toa widespread range of applications due to their ability toanalyse and capture the complexity and nonlinearity featuresof dynamic processes. One of the major applications of ANNsis a modelling or identification process of complex systems[26].

It is worth mentioning that the topology of the network isa crucial matter where as choosing the number of the neuronesand layers in the hidden zone is not an easy task. So far, nosystematic approach or automatic methods have been used totackle this issue. Because the network structure depends onthe nature and features of the process that would be modelled.Therefore, there are, probably, only two research methods toselect from, a blind or heuristic. The blind approach, or trialand error, is an unguided and arbitrary search method, to whichall possible alternatives are applied to find the optimal solution.Although this technique can eventually find the optimal ANNtopology with limited search space, this method is not practicalbecause it is considered highly expensive in terms of time andcomputations.

B. Particle Swarm Optimisation

Ever since particle swarm optimisation (PSO) has beenproposed by Kennedy and Eberhart in 1995 [27] and 2001[28], PSO algorithm turned to be vastly successful. The severalof researchers have presented the merit of the implementationof PSO as an optimiser for various applications [29]. In PSOprocedure, all individuals or particles (commonly between 10and 100) are located at a random position and are supposed tomove randomly in a defined direction in the search space. Eachparticle direction is then changed steadily to move assuredlyalong the direction of its best previous positions to discovereven a new better position according to certain criteria or anobjective function (fitness). The initial particle velocity andposition are selected arbitrarily, and the following velocityequation can update them as

V ci+1 = wVi+C1R1×(Pbi−xi)+C2R2×(Gb−xi) (13)

Whereas the new particle is calculated by adding the previousone to the new velocity as shown in the following equation:

xi+1 = xi + V ci+1 (14)

where: V c: velocity of the particle, X: position of the particle,R1, R2: independent random variables uniformly distributed in

[0, 1], C1, C2: acceleration coefficients as well as w: inertiaweight. Eq. 13 is used to compute the new velocity of theparticle according to its preceding velocity and the distancesof its current position from its own best position (Pb) andthe global best position (GB). Then, the particle moves toa new place in the search space, according to Eq. 14. Theperformance of each particle is measured according to a pre-defined objective function (performance index).

C. Hybrid System Design

Evolutionary-based optimisation, like PSO, can be appliedby only simple mathematical operations with a few lines ofcode [30]. This feature provides a low-cost method concerningboth memory and speed requirements. Thus, in this study, PSOis chosen to find the optimal network topology of the predictionmodel as depicted in Figure 2.

Fig. 2: Schematic diagram of the proposed hybrid system

IV. SIMULATION AND RESULTS

In this study, the reflux (L) and the boil-up (V) flow rateshad been used as inputs to the network while distillate and bot-tom composition chosen as outputs. The dataset implementedfor the training, validation and testing of ANN was generatedby applying 40 distributed random values, each lasting 50sampling time for (L) and (V) as shown in Figure 3. Thedistillate composition was approximately between 0.95 and1 (mole fraction), while the bottom composition was around0.005 to 0.12 (mole fraction) and a total of 2000 datasets werecollected for identification, Figure 4 presents the simulateddata of the column.

The dataset obtained by the simulation was randomlydivided into 70%, 15% and 15% for training, validationand testing respectively. Feedforward multilayer network hadbeen implemented to predict the product compositions ofthe distillation column. In addition, various backpropagationtraining algorithms, namely; Gradient Descent (GD), ScaledConjugate Gradient (SCG) and LevenbergMarquardt (LM)were separately applied to decide which one performs better


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Fig. 3: MATLAB/Simulink model of the distillation column

Time (Min)

0 500 1000 1500 2000

Reflux F

low

Rate

(K

mol/m

in)

1.22

1.24

1.26

1.28

1.3

1.32

1.34

(a) Reflux folw rate

Time (Min)

0 500 1000 1500 2000

Dis

tilla

te C

om

positio

n (

mole

fra

ction)

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

(b) Distillate composition

Time (Min)

0 500 1000 1500 2000

Bottom

Flo

w R

ate

(K

mol/m

in)

1.76

1.765

1.77

1.775

1.78

1.785

1.79

(c) Boil-up flow rate

than the others. Moreover, Log-sigmoid activation functionwas embedded in the neurones of the hidden layer(s) becauseof its differentiability. PSO was employed to find the optimalstructure of the network, the best operational parameters ofPSO algorithm were chosen after extensive simulations andwere set as following: For each of the network architecture,

No. of variables (dimensions) 2Size of the swarm (no. of particles) 50Maximum iterations (max) 100Cognitive acceleration (C1) 1.2Social acceleration (C2) 0.12Momentum or inertia (w) 0.9Minimum search space 1Maximum search space 25

the training algorithms had been run ten times with differentrandom initial weights and biases. After investigating the per-formance of different architectures using the PSO technique,a network with two hidden layers (including 23 neurons inthe first and 25 in the second) trained by LM algorithm have


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Time (Min)

0 500 1000 1500 2000

Bottom

s C

om

positio

n (

mole

fra

ction)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

(d) Bottoms composition

Fig. 4: Inputs/outputs of the simulation of the distillationcolumn

indicated reasonably good results. Figures 5 and 6 show theperformance of the network as a mean square error (MSE)versus the network architecture of the single and double hiddenlayer respectively. Table I demonstrates the training, testingand validation performances of different training approachesof both one and two layers in the hidden zone.

It is clearly indicated that much better results are found us-ing LM as training algorithm with two hidden layers topologybecause LM uses Hessian matrix approximation as a second-order method to calculate the change in gradient. Figures7 and 8 display regression plots of the network outputs onboth compositions of training and test sets. For a perfectfit, the data must fall along a 45-degree line, where thenetwork outputs are equal to the targets. The network with twohidden layers trained by LM algorithm, the fit, is reasonablygood of both datasets, with R values in each case of 0.99or above. Checking the test set is importantly required forexamining the generalisation of the network of unseen datain the learning stage. It is worth noting that the networktraining and simulation was performed using MATLAB R© andSimulink R© platform.

TrainingMethod

No. ofHiddenLayers

No. ofNeurones

TrainingMSE

TestingMSE

ValidationMSE

Time(sec)

GD1 4 3.972×

10−43.952×10−4

3.996×10−4

12.40

2 9 − 2 2.047×10−4

2.112×10−4

2.015×10−4

11.84

SCG1 19 1.529×

10−51.6 ×10−5

1.5 ×10−5

12.39

2 20 − 25 9.392×10−7

9.429×10−7

9.743×10−7

38.39

LM1 25 1.12 ×

10−61.225×10−6

1.195×10−6

18.58

2 23 − 25 4.365×10−9

3.984×10−9

7.8 ×10−9

11.37

TABLE I: Performances (MSE) of different PSO-ANN topolo-gies

0 5 10 15 20 25

MS

E

×10-3

0

2

4

6

8Gradient Descent

No. of Neurons

0 5 10 15 20 25

MS

E

×10-4

0

0.5

1

1.5

0 5 10 15 20 25

MS

E

×10-4

0

0.5

1

1.5Scaled Conjugate Gradient

Fig. 5: Performance curves of one hidden layer PSO-ANN ofdifferent algorithms

1st Hidden Layer

5

10

15

20

25

GD

25

20

2nd Hidden Layer

15

10

5

×10-3

5

0

6

4

3

2

1

Pe

rform

an

ce

MS

E

1st Hidden Layer

5

10

15

20

25

SCG

25

20

2nd Hidden Layer

15

10

5

×10-4

0

0.5

1

2

1.5

Perf

orm

ance M

SE


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5

1st Hidden Layer

1015

2025

LM

2520

2nd Hidden Layer

1510

5

×10-4

1

0.8

0.4

0.2

0

0.6

Perf

orm

an

ce M

SE

Fig. 6: Performance 3D surfaces of two hidden layers PSO-ANN of different algorithms

Target

0.93 0.94 0.95 0.96 0.97 0.98 0.99

Ou

tpu

t ~

= 1

*Targ

et

+ 2

.6e-0

5

0.93

0.94

0.95

0.96

0.97

0.98

0.99

Regression (xD): R=0.99999

Data

Fit

Y = T

(a) Distillate composition prediction

Target

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Ou

tpu

t ~

= 1

*Targ

et

+ 6

e-0

7

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Regression (xB): R=0.99998

Data

Fit

Y = T

(b) Bottoms composition prediction

Fig. 7: The regression line between predicted and simulatedcompositions of training set

Target

0.93 0.94 0.95 0.96 0.97 0.98 0.99

Ou

tpu

t ~

= 1

*Targ

et

+ -

7.3

e-0

5

0.93

0.94

0.95

0.96

0.97

0.98

0.99

Regression (xD): R=0.99999

Data

Fit

Y = T

(a) Distillate composition prediction

Target

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Ou

tpu

t ~

= 1

*Targ

et

+ 1

.6e-0

6

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Regression (xB): R=0.99999

Data

Fit

Y = T

(b) Bottoms composition prediction

Fig. 8: The regression line between predicted and simulatedcompositions of testing set

V. CONCLUSION

A PSO-based artificial neural network has been proposedas an intelligent prediction approach to estimate productcompositions of a binary distillation column; boil-up andreflux were used as inputs to the network. A double layerin the hidden zone with 23-25 neurones architecture waspresented the optimal performance of the prediction modelafter examining different training algorithms and topologiesusing particle swarm optimisation. the network trained by Lev-enbergMarquardt algorithm gave more accurate results withless MSE compared to Gradient Descent and Scaled ConjugateGradient. Therefore, the precision of predicted compositions ofthe distillation column using LM algorithm has shown to behigh, and the estimated compositions have approximately beenin agreement with the simulation results. The proposed ANNcould be used efficiently to improve the performance of thedifferent neural network controllers like NARMA-L2, directinverses and NN predictive controller, which mainly depend


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on the prediction performance, which is to be the subject offuture work.

ACKNOWLEDGMENT

The corresponding author is grateful to the Iraqi Ministryof Higher Education and Scientific Research for supporting thecurrent research.

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APPENDIX

Abbreviations, the operating conditions and technical as-pects of the distillation column are detailed in following table.

Symbol Description Value UnitN Number of trays 20 -NF Feed stage location 11 -F Typical inlet flow rate to the column 1 kmol/minD Typical distillate flow rate 0.5 kmol/minB Typical bottoms flow rate 0.5 kmol/minzF Light component in the feed (mole frac-

tion)0.5 -

qF Mole fraction of the liquid in the feed 1 -L Typical reflux flow rate 1.28 kmol/minV Typical boil-up flow rate 1.78 kmol/minα Relative volatility 2 -xD Distillate composition (mole fraction) 0.98 -xB Bottoms composition (mole fraction) 0.02 -i Stage number during distillation - -x Mole fraction of light component in

liquid- -

y Mole fraction of light component invapour

- -

M Tray hold-up liquid 0.5 kmolMD Condenser hold-up liquid 0.5 kmolMB Reboiler hold-up liquid 0.5 kmol


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